Stability versions are given of several inequalities from E. Lutwak's dual Brunn-Minkowski theory. These include the dual Aleksandrov-Fenchel inequality, the dual Brunn-Minkowski inequality, and the dual isoperimetric inequality. Two methods are used. One involves the application of strong forms of Clarkson's inequality for $L^p$ norms that hold for nonnegative functions, and the other utilizes a refinement of the arithmetic-geometric mean inequality. A new and more informative proof of the equivalence of the dual Brunn-Minkowski inequality and the dual Minkowski inequality is given. The main results are shown to be the best possible up to constant factors
Vassallo, S. F., Richard J., G., Stability of inequalities in the dual Brunn-Minkowski theory, <<JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS>>, 1999; (231): 568-587. [doi:10.1006/jmaa.1998.6254] [http://hdl.handle.net/10807/29349]
Stability of inequalities in the dual Brunn-Minkowski theory
Vassallo, Salvatore Flavio;
1999
Abstract
Stability versions are given of several inequalities from E. Lutwak's dual Brunn-Minkowski theory. These include the dual Aleksandrov-Fenchel inequality, the dual Brunn-Minkowski inequality, and the dual isoperimetric inequality. Two methods are used. One involves the application of strong forms of Clarkson's inequality for $L^p$ norms that hold for nonnegative functions, and the other utilizes a refinement of the arithmetic-geometric mean inequality. A new and more informative proof of the equivalence of the dual Brunn-Minkowski inequality and the dual Minkowski inequality is given. The main results are shown to be the best possible up to constant factorsI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.